Summary of the data

##  no_of_dependents         education    self_employed  income_annum    
##  Min.   :0.0       Graduate    :2144    No :2119     Min.   : 200000  
##  1st Qu.:1.0       Not Graduate:2125    Yes:2150     1st Qu.:2700000  
##  Median :3.0                                         Median :5100000  
##  Mean   :2.5                                         Mean   :5059124  
##  3rd Qu.:4.0                                         3rd Qu.:7500000  
##  Max.   :5.0                                         Max.   :9900000  
##   loan_amount         loan_term     cibil_score  residential_assets_value
##  Min.   :  300000   Min.   : 2.0   Min.   :300   Min.   : -100000        
##  1st Qu.: 7700000   1st Qu.: 6.0   1st Qu.:453   1st Qu.: 2200000        
##  Median :14500000   Median :10.0   Median :600   Median : 5600000        
##  Mean   :15133450   Mean   :10.9   Mean   :600   Mean   : 7472617        
##  3rd Qu.:21500000   3rd Qu.:16.0   3rd Qu.:748   3rd Qu.:11300000        
##  Max.   :39500000   Max.   :20.0   Max.   :900   Max.   :29100000        
##  commercial_assets_value luxury_assets_value bank_asset_value  
##  Min.   :       0        Min.   :  300000    Min.   :       0  
##  1st Qu.: 1300000        1st Qu.: 7500000    1st Qu.: 2300000  
##  Median : 3700000        Median :14600000    Median : 4600000  
##  Mean   : 4973155        Mean   :15126306    Mean   : 4976692  
##  3rd Qu.: 7600000        3rd Qu.:21700000    3rd Qu.: 7100000  
##  Max.   :19400000        Max.   :39200000    Max.   :14700000  
##     loan_status  
##   Approved:2656  
##   Rejected:1613  
##                  
##                  
##                  
## 

The summary() function provides a statistical summary of the entire dataset.

Data Pre-processing

We have removed unnecessary whitespaces from column names

Box plot of Number of Dependents and Loan Status

The box plot comparing the number of dependents and loan status reveals minimal variation. Both approved and rejected statuses exhibit similar distributions, with consistent median values. This suggests that the number of dependents has no significant impact on loan approval status.

Density plot of Loan Term based on Loan Status

The density plot highlights a clear relationship between loan approval/rejection and the loan term. Notably, applications with a term of 0-5 years show the highest approval rate, while those exceeding 5 years face more rejections. This pattern indicates a lending strategy favoring individuals capable of immediate repayment.

Scatter Plot of CIBIL Score vs Loan Amount

The scatter plot reveals a distinct correlation between loan amount and CIBIL score. Rejections are prominent in the CIBIL score range of 300-550, while approvals rise significantly beyond a CIBIL score of 550, even for loan amounts exceeding 35M.

Stacked Bar between Loan Status and Self Employment

The bar plot shows minimal differentiation in loan approval rates between self-employed and non-self-employed individuals, suggesting that self-employment may not be a decisive factor influencing loan approval.

Scatter Plot of Loan Amount vs Commercial assets value based on Loan Status

The scatter plot depicts a positive correlation between commercial asset value and loan amount, implying larger loans align with higher asset values. Similar distributions for approvals and rejections yield comparable approval and rejection rates for both commercial asset value and loan amount.

Scatter Loan Amount vs Residential Assets Value based on Loan Status

The graph indicates a positive correlation between residential asset value and loan amount, implying that higher residential values correspond to increased loan amounts. Similar distributions for approvals and rejections result in equal approval and rejection rates.

Scatter Plot of Loan Amount vs Luxury assets value based on Loan Status

The scatter plot reveals a positive correlation between luxury asset value and loan amount, suggesting that an increase in luxury asset value corresponds to higher loan amounts, with elevated chances of approval.

Scatter Plot of Loan Amount vs Bank Assets Value

Based on the graph, there is a positive correlation between luxury assets value and loan amount, indicating that as luxury assets value increases, so does the loan amount.

Scatter Plot of Loan Amount vs Income Per Annum based on Loan Status

The scatter plot indicates a direct correlation between annual income and loan amount, implying higher income aligns with larger loans. Approval and rejection rates appear consistent across different income and loan amount levels.

Box plot between Cibil Score vs Self Employed based on Loan Status

The box plot analysis indicates that CIBIL score significantly influences loan status, whereas self-employment status does not exhibit a notable impact.

Density Plot of Bank Assets grouped by Loan Status

Analyzing the density plot reveals a consistent loan status irrespective of bank assets, suggesting loan approval’s independence from bank assets sfluctuations.

Density Plot of CIBIL Score grouped by Loan Status

The density plot highlights that applicants with a higher CIBIL score (typically 500+) have a greater likelihood of loan approval, while applications with a score below that are rejected. This underscores the crucial role of a good CIBIL score and its significant impact on loan applications.

Correlation Plot

The correlation plot underscores the crucial link between cibil_score and loan_status, highlighting a strong correlation. Additionally, loan_amount shows noteworthy connections with various asset values, underscoring the importance of creditworthiness and financial factors in loan approval.

#STATISTICAL TEST

T-Test on Loan Status (Approval/Rejection) and Cibil Score

## 
##  Welch Two Sample t-test
## 
## data:  Approved$cibil_score and rejected$cibil_score
## t = 88, df = 4263, p-value <2e-16
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  268 280
## sample estimates:
## mean of x mean of y 
##       703       429

Null Hypothesis (\(H_{0}\)): CIBIL score has no significant association with loan status.

Alternate Hypothesis (\(H_{A}\)): CIBIL score has significant association with loan status.

The p-value \(0\), is very less than the standard alpha value of 0.05, hence, we reject the NULL hypothesis and conclude that CIBIL score has significant association with the probability of loan approval.

Chi-squared test between Education and Loan Status

## 
##  Pearson's Chi-squared test with Yates' continuity correction
## 
## data:  c
## X-squared = 0.08, df = 1, p-value = 0.8

Null Hypothesis (\(H_{0}\)): Education level and loan status are independent of each other.

Alternate Hypothesis (\(H_{A}\)): Education level and loan status are dependent on each other.

The high p-value of \(0.772\) for education level and loan status leads to the acceptance of the null hypothesis. Consequently, we conclude that an applicant’s education level has no significant impact on loan approval.

T-Test between Loan Status and Bank Asset Value

## 
##  Welch Two Sample t-test
## 
## data:  Approved$bank_asset_value and rejected$bank_asset_value
## t = -0.4, df = 3453, p-value = 0.7
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -245677  154809
## sample estimates:
## mean of x mean of y 
##   4959526   5004960

Null Hypothesis (\(H_{0}\)): Bank asset value and loan status are independent of each other.

Alternative Hypothesis (\(H_{A}\)): Bank asset value and loan status are dependent on each other.

Bank Asset Value and loan status have a high p-value of \(0.656\). Thus, we cannot reject the null hypothesis. We can therefore state that bank asset value and loan status are independent of each other and are not significantly associated.

T-Test between Loan Status and Resedential Assets Value

## 
##  Welch Two Sample t-test
## 
## data:  Approved$residential_assets_value and rejected$residential_assets_value
## t = -0.9, df = 3400, p-value = 0.3
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -595310  209937
## sample estimates:
## mean of x mean of y 
##   7399812   7592498

Null Hypothesis (\(H_{0}\)): There is no significant association between the values of residential asset and loan approval status.

Alternative Hypothesis (\(H_{A}\)): There is a significant association between the values of residential asset and loan approval status.

With a p-value of \(0.348\), we cannot reject the null hypothesis and thus, we conclude from the null hypothesis that there exists no significant association between residential assets value and loan status.

T-test between number of dependents and loan status

## 
##  Welch Two Sample t-test
## 
## data:  Approved$no_of_dependents and rejected$no_of_dependents
## t = -1, df = 3400, p-value = 0.2
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -0.1683  0.0416
## sample estimates:
## mean of x mean of y 
##      2.47      2.54

Null Hypothesis (\(H_{0}\)): There is no significant association between the number of dependents and loan approval status.

Alternative Hypothesis (\(H_{A}\)): There is a significant association between the number of dependents and loan approval status.

With a p-value of \(0.237\), we fail to reject the null hypothesis. Therefore, we can conclude that there is no significant association between the number of dependents and loan status.

T-test between luxury assets value and loan status

## 
##  Welch Two Sample t-test
## 
## data:  a$luxury_assets_value and r$luxury_assets_value
## t = -1, df = 3442, p-value = 0.3
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -851752  271073
## sample estimates:
## mean of x mean of y 
##  15016604  15306944

Null Hypothesis (\(H_{0}\)): The luxury assets value of an applicant has no significant association with their loan status.

Alternate Hypothesis (\(H_{A}\)): The luxury assets value of an applicant has significant association with their loan status.

With a p-value of \(0.311\), we cannot reject the null hypothesis and thus, we conclude that the luxury assets value of an applicant has no significant association with their loan status.

## Pearson Correlation Coefficient: 0.00844

## p-value: 0.582

The low Pearson correlation coefficient \(0.008\) indicates a weak relationship between loan_term and loan_amount. Moreover, the high p-value \(0.582\) suggests the observed correlation is not statistically significant.

Regression problem

## Reordering variables and trying again:

## Subset selection object
## Call: regsubsets.formula(loan_amount ~ ., data = data, nvmax = 10, 
##     nbest = 2, method = "exhaustive")
## 12 Variables  (and intercept)
##                          Forced in Forced out
## no_of_dependents             FALSE      FALSE
## educationNot Graduate        FALSE      FALSE
## self_employedNo              FALSE      FALSE
## income_annum                 FALSE      FALSE
## loan_term                    FALSE      FALSE
## cibil_score                  FALSE      FALSE
## residential_assets_value     FALSE      FALSE
## commercial_assets_value      FALSE      FALSE
## luxury_assets_value          FALSE      FALSE
## bank_asset_value             FALSE      FALSE
## loan_statusRejected          FALSE      FALSE
## self_employedOther           FALSE      FALSE
## 2 subsets of each size up to 11
## Selection Algorithm: exhaustive
##           no_of_dependents educationNot Graduate self_employedNo
## 1  ( 1 )  " "              " "                   " "            
## 1  ( 2 )  " "              " "                   " "            
## 2  ( 1 )  " "              " "                   " "            
## 2  ( 2 )  " "              " "                   " "            
## 3  ( 1 )  " "              " "                   " "            
## 3  ( 2 )  " "              " "                   " "            
## 4  ( 1 )  " "              " "                   " "            
## 4  ( 2 )  "*"              " "                   " "            
## 5  ( 1 )  "*"              " "                   " "            
## 5  ( 2 )  " "              " "                   " "            
## 6  ( 1 )  "*"              " "                   " "            
## 6  ( 2 )  "*"              " "                   " "            
## 7  ( 1 )  "*"              " "                   " "            
## 7  ( 2 )  "*"              " "                   " "            
## 8  ( 1 )  "*"              " "                   " "            
## 8  ( 2 )  "*"              " "                   " "            
## 9  ( 1 )  "*"              " "                   " "            
## 9  ( 2 )  "*"              " "                   "*"            
## 10  ( 1 ) "*"              " "                   "*"            
## 10  ( 2 ) "*"              "*"                   " "            
## 11  ( 1 ) "*"              "*"                   "*"            
## 11  ( 2 ) "*"              " "                   "*"            
##           self_employedOther income_annum loan_term cibil_score
## 1  ( 1 )  " "                "*"          " "       " "        
## 1  ( 2 )  " "                " "          " "       " "        
## 2  ( 1 )  " "                "*"          " "       " "        
## 2  ( 2 )  " "                "*"          " "       " "        
## 3  ( 1 )  " "                "*"          " "       "*"        
## 3  ( 2 )  " "                "*"          " "       " "        
## 4  ( 1 )  " "                "*"          " "       "*"        
## 4  ( 2 )  " "                "*"          " "       "*"        
## 5  ( 1 )  " "                "*"          " "       "*"        
## 5  ( 2 )  " "                "*"          "*"       "*"        
## 6  ( 1 )  " "                "*"          "*"       "*"        
## 6  ( 2 )  " "                "*"          " "       "*"        
## 7  ( 1 )  " "                "*"          "*"       "*"        
## 7  ( 2 )  " "                "*"          "*"       "*"        
## 8  ( 1 )  " "                "*"          "*"       "*"        
## 8  ( 2 )  " "                "*"          "*"       "*"        
## 9  ( 1 )  " "                "*"          "*"       "*"        
## 9  ( 2 )  " "                "*"          "*"       "*"        
## 10  ( 1 ) " "                "*"          "*"       "*"        
## 10  ( 2 ) " "                "*"          "*"       "*"        
## 11  ( 1 ) " "                "*"          "*"       "*"        
## 11  ( 2 ) "*"                "*"          "*"       "*"        
##           residential_assets_value commercial_assets_value luxury_assets_value
## 1  ( 1 )  " "                      " "                     " "                
## 1  ( 2 )  " "                      " "                     "*"                
## 2  ( 1 )  " "                      " "                     " "                
## 2  ( 2 )  " "                      "*"                     " "                
## 3  ( 1 )  " "                      " "                     " "                
## 3  ( 2 )  " "                      "*"                     " "                
## 4  ( 1 )  " "                      "*"                     " "                
## 4  ( 2 )  " "                      " "                     " "                
## 5  ( 1 )  " "                      "*"                     " "                
## 5  ( 2 )  " "                      "*"                     " "                
## 6  ( 1 )  " "                      "*"                     " "                
## 6  ( 2 )  "*"                      "*"                     " "                
## 7  ( 1 )  "*"                      "*"                     " "                
## 7  ( 2 )  " "                      "*"                     "*"                
## 8  ( 1 )  "*"                      "*"                     "*"                
## 8  ( 2 )  "*"                      "*"                     " "                
## 9  ( 1 )  "*"                      "*"                     "*"                
## 9  ( 2 )  "*"                      "*"                     "*"                
## 10  ( 1 ) "*"                      "*"                     "*"                
## 10  ( 2 ) "*"                      "*"                     "*"                
## 11  ( 1 ) "*"                      "*"                     "*"                
## 11  ( 2 ) "*"                      "*"                     "*"                
##           bank_asset_value loan_statusRejected
## 1  ( 1 )  " "              " "                
## 1  ( 2 )  " "              " "                
## 2  ( 1 )  " "              "*"                
## 2  ( 2 )  " "              " "                
## 3  ( 1 )  " "              "*"                
## 3  ( 2 )  " "              "*"                
## 4  ( 1 )  " "              "*"                
## 4  ( 2 )  " "              "*"                
## 5  ( 1 )  " "              "*"                
## 5  ( 2 )  " "              "*"                
## 6  ( 1 )  " "              "*"                
## 6  ( 2 )  " "              "*"                
## 7  ( 1 )  " "              "*"                
## 7  ( 2 )  " "              "*"                
## 8  ( 1 )  " "              "*"                
## 8  ( 2 )  "*"              "*"                
## 9  ( 1 )  "*"              "*"                
## 9  ( 2 )  " "              "*"                
## 10  ( 1 ) "*"              "*"                
## 10  ( 2 ) "*"              "*"                
## 11  ( 1 ) "*"              "*"                
## 11  ( 2 ) "*"              "*"

The regsubsets() identifies the optimal subset of predictor variables by minimizing or maximizing selected criteria like Adjusted R-squared (adjr2), R-squared (r2), Bayesian Information Criterion (BIC), or Mallows’ Cp.

In case of the Adjusted R-squared plot, the best possible set of predictors are found to be: no_of_dependents, loan_term, income_annum, commercial_assests_value, cibil_score and loan_status. In case of the R-squared plot, the best possible set of predictors are found to be: no_of_dependents, loan_term, income_annum, commercial_assests_value, cibil_score and loan_status. From the BIC plot we can observe that the best possible set of predictors are found to be: no_of_dependents, loan_term, income_annum, residential_assets_value, commercial_assests_value, cibil_score and loan_status. From the Cp Mallow plot we can observe that the best possible set of predictors are found to be: no_of_dependents, income_annum, residential_assets_value, commercial_assests_value, cibil_score and loan_status.

##                          Abbreviation
## no_of_dependents                    n
## educationNot Graduate              eG
## self_employedNo                   s_N
## income_annum                        i
## loan_term                         ln_
## cibil_score                       cb_
## residential_assets_value            r
## commercial_assets_value           c__
## luxury_assets_value               l__
## bank_asset_value                    b
## loan_statusRejected               l_R
## self_employedOther                s_O

From the Adjusted R-squared statistic plot, the most suitable set of predictors are found to be: no_of_dependents, loan_term, income_annum, commercial_assests_value, cibil_score, commercial_assests_value, luxury_assests_value and loan_status.

##                          Abbreviation
## no_of_dependents                    n
## educationNot Graduate              eG
## self_employedNo                   s_N
## income_annum                        i
## loan_term                         ln_
## cibil_score                       cb_
## residential_assets_value            r
## commercial_assets_value           c__
## luxury_assets_value               l__
## bank_asset_value                    b
## loan_statusRejected               l_R
## self_employedOther                s_O

The most relevant predictors from the Mallow Cp plot are found to be no_of_dependents, income_annum, commercial_assests_value, cibil_score and loan_status.

Classification Problem

## Fitting algorithm:  AIC-glm
## Best Model:
##              df deviance
## Null Model 4262     1880
## Full Model 4268     5661
## 
##  likelihood-ratio test - GLM
## 
## data:  H0: Null Model vs. H1: Best Fit AIC-glm
## X = 3780, df = 6, p-value <2e-16

##   no_of_dependents education self_employed income_annum loan_amount loan_term
## 1            FALSE     FALSE         FALSE         TRUE        TRUE      TRUE
## 2            FALSE     FALSE         FALSE         TRUE        TRUE      TRUE
## 3            FALSE     FALSE         FALSE         TRUE        TRUE      TRUE
## 4            FALSE      TRUE         FALSE         TRUE        TRUE      TRUE
## 5            FALSE     FALSE         FALSE         TRUE        TRUE      TRUE
##   cibil_score residential_assets_value commercial_assets_value
## 1        TRUE                    FALSE                   FALSE
## 2        TRUE                    FALSE                   FALSE
## 3        TRUE                    FALSE                    TRUE
## 4        TRUE                    FALSE                   FALSE
## 5        TRUE                    FALSE                    TRUE
##   luxury_assets_value bank_asset_value Criterion
## 1                TRUE             TRUE      1892
## 2                TRUE            FALSE      1893
## 3                TRUE             TRUE      1893
## 4                TRUE             TRUE      1894
## 5                TRUE            FALSE      1894

##  no_of_dependents education       self_employed   income_annum   loan_amount   
##  Mode :logical    Mode :logical   Mode :logical   Mode:logical   Mode:logical  
##  FALSE:5          FALSE:4         FALSE:5         TRUE:5         TRUE:5        
##                   TRUE :1                                                      
##                                                                                
##                                                                                
##                                                                                
##  loan_term      cibil_score    residential_assets_value commercial_assets_value
##  Mode:logical   Mode:logical   Mode :logical            Mode :logical          
##  TRUE:5         TRUE:5         FALSE:5                  FALSE:3                
##                                                         TRUE :2                
##                                                                                
##                                                                                
##                                                                                
##  luxury_assets_value bank_asset_value   Criterion   
##  Mode:logical        Mode :logical    Min.   :1892  
##  TRUE:5              FALSE:2          1st Qu.:1893  
##                      TRUE :3          Median :1893  
##                                       Mean   :1893  
##                                       3rd Qu.:1894  
##                                       Max.   :1894

Train Test Split

The dataset was initially examined for the distribution of the target variable, loan_status (indicating loan approval). To promote model generalization, the data was later divided into training (80%) and test (20%) sets, ensuring reproducibility with a specified seed.

## 
## Approved Rejected 
##     2656     1613

## Rejected 
##    0.378

## [1] 0.8

## [1] 3415

## [1] 854

Regression

## 
## Call:
## lm(formula = loan_amount ~ no_of_dependents + loan_term + income_annum + 
##     commercial_assets_value + cibil_score + loan_status, data = data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -9773675 -1894729   -32406  2008070 10051244 
## 
## Coefficients:
##                          Estimate Std. Error t value Pr(>|t|)    
## (Intercept)              2.02e+06   3.60e+05    5.62  2.0e-08 ***
## no_of_dependents        -4.88e+04   3.03e+04   -1.61    0.108    
## loan_term                9.14e+03   9.17e+03    1.00    0.319    
## income_annum             2.96e+00   2.39e-02  123.95  < 2e-16 ***
## commercial_assets_value  3.02e-02   1.53e-02    1.98    0.048 *  
## cibil_score             -2.51e+03   4.73e+02   -5.30  1.2e-07 ***
## loan_statusRejected     -1.26e+06   1.69e+05   -7.41  1.5e-13 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 3360000 on 4262 degrees of freedom
## Multiple R-squared:  0.862,  Adjusted R-squared:  0.862 
## F-statistic: 4.45e+03 on 6 and 4262 DF,  p-value: <2e-16

## Training R-squared: 0.862

## Testing R-squared: 0.862

Classification

## 
## Call:
## glm(formula = loan_status ~ no_of_dependents + income_annum + 
##     loan_amount + loan_term + cibil_score + luxury_assets_value + 
##     bank_asset_value, family = "binomial", data = data_train)
## 
## Coefficients:
##                      Estimate Std. Error z value Pr(>|z|)    
## (Intercept)          1.13e+01   4.76e-01   23.67  < 2e-16 ***
## no_of_dependents     6.60e-03   3.85e-02    0.17     0.86    
## income_annum         5.26e-07   9.54e-08    5.51  3.5e-08 ***
## loan_amount         -1.33e-07   1.99e-08   -6.72  1.9e-11 ***
## loan_term            1.49e-01   1.27e-02   11.72  < 2e-16 ***
## cibil_score         -2.46e-02   9.24e-04  -26.59  < 2e-16 ***
## luxury_assets_value -2.66e-08   1.97e-08   -1.35     0.18    
## bank_asset_value    -3.98e-08   3.63e-08   -1.10     0.27    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 4528.9  on 3414  degrees of freedom
## Residual deviance: 1531.7  on 3407  degrees of freedom
## AIC: 1548
## 
## Number of Fisher Scoring iterations: 7

## [1] "Training Accuracy: 91.45 %"

## [1] "Test Accuracy: 93.09 %"

## [1] "Training Precision: 88.92 %"

## [1] "Training Recall: 88.51 %"

## [1] "Test Precision: 90.68 %"

## [1] "Test Recall: 90.97 %"

## 'log Lik.' 0.729 (df=8)

Data preprocessing

## 'data.frame':    3415 obs. of  14 variables:
##  $ no_of_dependents        : int  3 3 2 3 5 4 3 3 3 5 ...
##  $ education               : Factor w/ 2 levels "Graduate","Not Graduate": 2 1 1 1 1 1 2 1 2 2 ...
##  $ self_employed           : num  2 1 2 2 1 2 2 2 1 1 ...
##  $ income_annum            : int  1600000 6700000 4700000 8000000 4200000 8700000 3800000 5500000 6200000 2700000 ...
##  $ loan_amount             : int  3900000 13400000 14000000 26200000 9400000 32100000 11400000 11600000 14600000 6800000 ...
##  $ loan_term               : int  20 14 12 16 6 8 4 6 2 6 ...
##  $ cibil_score             : int  804 782 784 890 678 397 323 745 664 461 ...
##  $ residential_assets_value: int  900000 4900000 13400000 15800000 4700000 8900000 5800000 9400000 18300000 4500000 ...
##  $ commercial_assets_value : int  2500000 4000000 2700000 4300000 5500000 17000000 4000000 8000000 8400000 2000000 ...
##  $ luxury_assets_value     : int  3200000 25800000 14800000 25000000 9900000 34700000 9600000 12800000 16800000 8200000 ...
##  $ bank_asset_value        : int  800000 9600000 6900000 4000000 5700000 4800000 4400000 5400000 6600000 1700000 ...
##  $ loan_status             : Factor w/ 2 levels "Approved","Rejected": 1 1 1 1 1 2 1 1 1 2 ...
##  $ prediction              : num  0.00512 0.0057 0.00193 0.00025 0.01819 ...
##  $ prob                    : num  0.00512 0.0057 0.00193 0.00025 0.01819 ...

KNN Model creation

##  num [1:2, 1:11] 1 0.542 3 0.573 5 ...

KNN Evaluation metrices

##           Actual
## Predicted  Approved Rejected
##   Approved     1855      980
##   Rejected      269      311

## [1] "Training Accuracy: 63.43 %"

##  Factor w/ 2 levels "Approved","Rejected": 1 1 1 1 1 2 1 1 2 2 ...

## [1] 854

## bank_18NN
## Approved Rejected 
##      704      150

## [1] "Test Accuracy: 61.12 %"

## 
##  
##    Cell Contents
## |-------------------------|
## |                       N |
## |           N / Row Total |
## |           N / Col Total |
## |         N / Table Total |
## |-------------------------|
## 
##  
## Total Observations in Table:  854 
## 
##  
##                            | bank_18NN 
## data_test[, "loan_status"] |  Approved |  Rejected | Row Total | 
## ---------------------------|-----------|-----------|-----------|
##                   Approved |       452 |        80 |       532 | 
##                            |     0.850 |     0.150 |     0.623 | 
##                            |     0.642 |     0.533 |           | 
##                            |     0.529 |     0.094 |           | 
## ---------------------------|-----------|-----------|-----------|
##                   Rejected |       252 |        70 |       322 | 
##                            |     0.783 |     0.217 |     0.377 | 
##                            |     0.358 |     0.467 |           | 
##                            |     0.295 |     0.082 |           | 
## ---------------------------|-----------|-----------|-----------|
##               Column Total |       704 |       150 |       854 | 
##                            |     0.824 |     0.176 |           | 
## ---------------------------|-----------|-----------|-----------|
## 
## 

## Confusion Matrix and Statistics
## 
##           Reference
## Prediction Approved Rejected
##   Approved      452      252
##   Rejected       80       70
##                                         
##                Accuracy : 0.611         
##                  95% CI : (0.578, 0.644)
##     No Information Rate : 0.623         
##     P-Value [Acc > NIR] : 0.771         
##                                         
##                   Kappa : 0.075         
##                                         
##  Mcnemar's Test P-Value : <2e-16        
##                                         
##             Sensitivity : 0.850         
##             Specificity : 0.217         
##          Pos Pred Value : 0.642         
##          Neg Pred Value : 0.467         
##              Prevalence : 0.623         
##          Detection Rate : 0.529         
##    Detection Prevalence : 0.824         
##       Balanced Accuracy : 0.534         
##                                         
##        'Positive' Class : Approved      
## 

## [1] "Precision: 0.64"

## [1] "Recall: 0.85"

Decision Tree model

## [1] "Train Accuracy: 96.81 %"

## [1] "Test Accuracy: 96.49 %"

## Confusion Matrix and Statistics
## 
##           Reference
## Prediction Approved Rejected
##   Approved      529       27
##   Rejected        3      295
##                                        
##                Accuracy : 0.965        
##                  95% CI : (0.95, 0.976)
##     No Information Rate : 0.623        
##     P-Value [Acc > NIR] : < 2e-16      
##                                        
##                   Kappa : 0.924        
##                                        
##  Mcnemar's Test P-Value : 2.68e-05     
##                                        
##             Sensitivity : 0.994        
##             Specificity : 0.916        
##          Pos Pred Value : 0.951        
##          Neg Pred Value : 0.990        
##              Prevalence : 0.623        
##          Detection Rate : 0.619        
##    Detection Prevalence : 0.651        
##       Balanced Accuracy : 0.955        
##                                        
##        'Positive' Class : Approved     
## 

## [1] "Precision: 0.95"

## [1] "Recall: 0.99"

## AUC: 0.955

## [1] "AUC score of KNN 0.533507682249101"

## [1] "AUC score of decision Tress 0.95525498528931"

## [1] "AUC score of Logistic regressor 0.96766802184032"

Random forest

## 
## Call:
##  randomForest(formula = loan_status ~ no_of_dependents + income_annum +      loan_amount + loan_term + cibil_score + luxury_assets_value +      bank_asset_value, data = data_train, ntree = 500, importance = TRUE) 
##                Type of random forest: classification
##                      Number of trees: 500
## No. of variables tried at each split: 2
## 
##         OOB estimate of  error rate: 1.58%
## Confusion matrix:
##          Approved Rejected class.error
## Approved     2108       16     0.00753
## Rejected       38     1253     0.02943

• The confusion matrix indicates strong performance in predicting both “Approved” and “Rejected” classes.
• Class error rates are low, with 0.75% for “Approved” and 2.94% for “Rejected,” showcasing accurate predictions.
• The model’s ability to correctly identify instances is evident from the high numbers on the diagonal of the confusion matrix.

Overall, the random forest model proves effective in classifying loan applications based on provided features, demonstrating a low out-of-bag error rate.

##                     Approved Rejected MeanDecreaseAccuracy MeanDecreaseGini
## no_of_dependents        1.33     4.34                 3.74             15.8
## income_annum           15.75    14.63                21.43             37.2
## loan_amount            26.23    17.25                32.05             58.8
## loan_term              87.47    80.78               103.77             95.8
## cibil_score           383.23   399.68               440.78           1328.5
## luxury_assets_value    12.77    10.13                16.37             38.7
## bank_asset_value       10.79     9.59                14.86             29.8

Model metrics random forest

## [1] "Train Accuracy: 100 %"

## [1] "Test Accuracy: 98.59 %"

## [1] "Precision: 0.97"

## [1] "Recall: 0.99"

## AUC: 0.983

## [1] "AUC score of KNN 0.533507682249101"

## [1] "AUC score of decision Tress 0.95525498528931"

## [1] "AUC score of Logistic regressor 0.96766802184032"

## [1] "AUC score of Random Forest 0.983205295848316"

Model Result chart

• Random Forest: Achieving the highest AUC score of 98.321%, the Random Forest model demonstrates superior discriminative capability. This underscores its suitability for the given classification task.

• Logistic Regression: With an AUC score of 96.767%, Logistic Regression performs admirably and proves to be a robust model for the task.

• Decision Tree: The Decision Tree model yields a respectable AUC score of 95.525%, positioning it as a viable choice for classification.

• KNN: While KNN lags behind the other models with an AUC score of 53.351%, its performance is noteworthy and may still be relevant depending on the specific requirements of the application.